BRUSSELS (Reuters) - The number of Syrians trying to enter the European Union illegally increased five-fold last year, an EU agency said on Thursday, as refugees fled their war-ravaged country.

Almost 8,000 Syrians without papers, and some with false passports, attempted to cross the Greek and Bulgarian borders to reach wealthy nations such as Germany and Sweden, said the EU's Frontex agency, which oversees the bloc's border controls.

That compared to 1,600 people in 2011, Frontex said.

A two-year old uprising against Syrian President Bashar al-Assad has forced 1.3 million people to seek refuge abroad. The violence has destroyed homes and shattered historic cities, as well as killing more than 80,000 people.

Along with Afghans, undocumented Syrians are the most numerous nationality at the Greek border with Turkey, Frontex said.

Most flee Syria by bus and car through Turkey and enter through Greece by land or sea as well as across Turkey's land border with Bulgaria.

Greece has long been the main gateway into the EU for migrants from the Middle East, but tougher Greek border controls brought on by the country's economic crisis mean more Syrians are trying to go through Bulgaria.

Once they reach the European Union, most Syrians apply for asylum in Sweden or Germany which give Syrians automatic refugee status or protection upon arrival.

(Reporting by Teddy Nykiel; Editing by Jon Hemming)